In the process of packaging pieces of meat and other products, it is desirable to place a sheet of paper or other separating material between adjacent pieces in a package to prevent the pieces from sticking together. Interleaving machines are known which shear sheets of paper from a roll, usually by piercing the paper when it is supported by a resilient surface, and place each sheet in contact with a product to be packaged. However, the paper cutting devices quickly become dull, thus requiring frequent machine shutdowns while the cutting device is sharpened or replaced. In addition, the interleaver machine must also be stopped when the paper roll empties and must be changed, or when there is some other interruption in the supply of paper. Furthermore, in feeding paper from the roll to the cutting device, problems have existed with respect to permitting the paper to unwind freely from the paper roll without producing an excess of slack in the web of paper being fed. Other problems have existed in precisely aligning the sheets of paper with the pieces of meat. It is also desirable to provide a mechanism for controlling the quality of the meat being packaged so that undersized pieces of meat are removed from the interleaver before they are papered and packaged.